The graph of y = x4 – 2x2 + 1 is shown.

On a coordinate plane, a curved line has two minimum values at (negative 1, 0) and (1, 0) and one maximum value. Point A is at (negative 0.5, 0.5), point B is at (0, 1), point C is at (1, 0), and point D is at (1.6, 3).

Which point is a relative maximum?

A
B
C
D

Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.

数学思维是如何建立的？ 怎样才能有数学思维？

Answer:

26

Step-by-step explanation:

the whole area is the sum of the area of the rectangle in the middle and the 2 triangles on either side of the rectangle.

sBC = distance between (0,3) and (4,-1)

and that is the Pythagoras calculation with the coordinate differences

sBC² = (4-0)² + (-1 - 3)² = 16 + 16 = 32

sBC = sqrt(32) = sFE

to get the area of the rectangle we need also FB (or CE).

sFB² = (0 - -2)² + (3-1)² = 4 + 4 = 8

sFB = sqrt(8) = sCE

area of rectangle is

sBC×sFB = sqrt(32)×sqrt(8) = sqrt(32×8) = sqrt(256) = 16

the area of a right-angled triangle is

a×b/2

we have sFB and need sAF

sAF² = (-5 - -2)² + (4-1)² = 9 + 9 = 18

sAF = sqrt(18)

the area of the left triangle is

sFB×sAF/2 = sqrt(8)×sqrt(18)/2 = sqrt(8×18)/2 = sqrt(144)/2 = 12/2 = 6

for the right triangle we have sCE and need sED.

sED² = (2 - 4)² + (-3 - -5)² = 4 + 4 = 8

sED = sqrt(8)

the area of the right triangle is

sCE×sED/2 = sqrt(8)×sqrt(8)/2 = 8/2 = 4

so in total we have for the area

16 + 6 + 4 = 26

Answer:

x ≥-24

Step-by-step explanation:

3 - x/2 ≥ 15

Subtract 3 from each side

3-3 - x/2 ≥ 15-3

-x/2 ≥12

Multiply by -2

-x/2 * -2 ≥12 *-2

x ≥-24

Answer:

A. x ≤ 24

Step-by-step explanation:

multiply both side by 2 . Since 2 is the positive the inequality direction remains the same.

subtract 6 from both sides

Divide both side by - 1. Since -1 is negative, the inequality direction remains the change.

Answer:

103.23 square feet

Step-by-step explanation:

Area of the largest room = length × width

Each centimeter was equal to 1.5 feet

7.4 cm = 1.5 × 7.4 = 11.1 feet

6.2 cm = 1.5 × 6.2 = 9.3 feet

Length = 11.1 feet

Width = 9.3 feet

Area of the largest room = length × width

= 11.1 feet × 9.3 feet

= 103.23 square feet

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

[tex]m=(x+6)\times 10+x\times 1[/tex]

[tex]m=10x+60+x[/tex]

[tex]m=11x+60[/tex]

If we interchange the digits, then the value of new number is:

[tex]n=x\times 10+(x+6)\times 1[/tex]

[tex]n=10x+x+6[/tex]

[tex]n=11x+6[/tex]

The sum of the new and the original number is 132.

[tex]m+n=132[/tex]

[tex]11x+60+11x+6=132[/tex]

[tex]22x+66=132[/tex]

[tex]22x=132-66[/tex]

[tex]22x=66[/tex]

Divide both sides by 22.

[tex]x=\dfrac{66}{22}[/tex]

[tex]x=3[/tex]

So, the unit digit of the original number is 3 and the tens digit is:

[tex]x+6=3+6[/tex]

[tex]x+6=9[/tex]

Therefore, the original number is 39.

Step-by-step explanation:

40+24+11+8+17= 100

100 - 700

24 - ?

24×700/100

= 168 visitors ordered apple juice

100-700

11-?

11×700/100

=77 people ordered grape juice

Answer:i don’t know

Step-by-step explanation:i don’t know

Answer:Steve age will be 15 y.o

Step-by-step explanation:

Answer:

Velocity in still air: 760 mi/ hr

Velocity against the wind: 210 mi/ hr

Step-by-step explanation:

Given

See attachment for complete question

Required

The rate in still air

The rate of the wind

From the question, the velocity (v) against the wind is:

[tex]v =\frac{distance}{time}[/tex]

[tex]v =\frac{3040}{4}[/tex]

[tex]v_1 =760mi/hr[/tex]

The velocity with the wind is:

[tex]v_2 = \frac{8260}{7}[/tex]

[tex]v_2 = 1180mi/hr[/tex]

Let:

[tex]x \to[/tex] velocity in still air

[tex]y \to[/tex] velocity of the wind

So, we have:

[tex]x - y = 760[/tex]

[tex]x + y = 1180[/tex]

Add both equations

[tex]x + x -y + y = 760 + 1180[/tex]

[tex]2x = 1940[/tex]

Divide by 2

[tex]x = 970[/tex]

Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]

[tex]970 - y= 760[/tex]

Make y the subject

[tex]y = 970 - 760[/tex]

[tex]y = 210[/tex]

Answer:

120 * 0.90 = 108 km

Step-by-step explanation:

Answer:

108km

Step-by-step explanation:

Answer:

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes 4 2 3 5 5 3 1

Juice (milliliters) 177 234 202 140 155 210 265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice

Step-by-step explanation:

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes             4        2      3        5       5      3        1

Juice (milliliters)  177    234   202   140   155   210   265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

To learn more about the data visit:

https://brainly.com/question/19243813

#SPJ2

The values that complete the table are -14, -8, -2 and 4

Given the function y = 3x - 8, we are to complete the given table.

If x = -2

y = 3(-2) - 8

y = -14

If x = 0

y = 3(0) - 8

y = -8

If x = 2

y = 3(2) - 8

y = -2

If x = 4

y = 3(4) - 8

y = 4

Hence the values that complete the table are -14, -8, -2 and 4

Learn more on table of functions here: https://brainly.com/question/3632175

Answer:

5/12

Step-by-step explanation:

1/2 x 5/6 = 5/12

Answer:

(S-2πr^2)/ 2πr = h

Step-by-step explanation:

S = 2πrh + 2πr^2

Subtract 2 pi r^2 from each side

S-2πr^2  = 2πrh + 2πr^2 -2πr^2

S-2πr^2  = 2πrh

Divide each side by 2 pi r

(S-2πr^2)/ 2πr = 2πrh/2πr

(S-2πr^2)/ 2πr = h

It is given that,

→ S = 2πrh + 2πr²

Now subtract 2πr² from the both sides,

→ S - 2πr² = 2πrh + 2πr² - 2πr²

→ S - 2πr² = 2πrh

Then divide both sides by 2πr,

→ (S-2πr²)/2πr = 2πrh/2πr

→ (S-2πr²)/2πr = h

Hence, (S-2πr²)/2πr = h is the result.

Answer:

10 plants

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.

Answer:

40 degrees

Step-by-step explanation:

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

Answer:

The answer is B

Answer:

zero point six hundred and four

Step-by-step explanation:

Answer:

7B + (36 * 4) = 184

Step-by-step explanation:

In a family restaurant there are 36 tables and 7 booths.

Each table can seat 4 people.

Let the number of people who can be seated in a booth be represented by B.

Total seating capacity of the restaurant is 184 people.

Expressing this as an equation:

Among the given options, this relation is expressed in the second option, namely, 7B + (36 * 4) = 184

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

Answer:

-1

Step-by-step explanation:

we match the input to the output to find that f(3) points towards -1

Answer:

7.Mean=Ex/n

= 88+96+92+84+86+92+98/7

=90

(b). Median = {84,86,88},92,{92,96,98}

=92

(C).Mode=92 ; it is the number with the highest frequency

9.Mean=Ex/n

=28+26+32+24+27+32+29/7

=28

(b).Median={24,26,27},28,{29,32,32}

=28

(c).Mode=32;it is the number with the highest frequency.

8.Mean=Ex/n

=3.5+5.7+9.8+7+12.4+10.2/6

=8.1

(b).Median={3.5,5.7},7,9.8,{10.2,12.4}

=7+9.8/2

=8.4

(c).Mode=no mode

10.Mean=Ex/n

=2+6+9+8+8+2+8+7+5+4/10

=5.9

(b).Median={2,2,4,5},6,7,{8,8,8,9}

=6+7/2

=6.5

(c).Mode= 8;it is the number with the highest frequency.

I hope this helps.

Given,

d = 2t

here, t = 25

Therefore,

d = 2*25

= 50m

Answer:

35 degrees

Step-by-step explanation:

since both sides are equal, so are the angles involved.

Answer:

commutative property of addition.

a sequence of additions can be done in any order and the total remains the same.

Step-by-step explanation:

so, we can actually do

27 + 3 + 15 + 5

and now it is easy to combine 27+3 to 30 and 15+5 to 20, and to make the final calculation of 30 + 20 = 50 in our minds.